Abstract
A passive method of realizing nonreciprocal wave propagation in a two-dimensional (2D) lattice is proposed, using bilinear springs combined with the necessary spatial asymmetry to provide a stable and strong departure from reciprocity. The bilinear property is unique among nonlinear mechanisms in that it is independent of amplitude but sensitive to the sign of the wave motion; the 2D setup allows the flexibility of generating spatial asymmetry at both small and large scales. The starting point is a linear 2D monatomic spring–mass lattice with strong directionally dependent wave propagation. The source and receiver are aligned so that there is virtually no direct wave transmission between them. Adding a region of bilinearity combined with spatial asymmetry that is not in the direct path between the source and receiver causes signal transmission via nonreciprocal scattering. A variety of spatially asymmetric bilinear configurations are considered, ranging from compact modulations confined within the unit cell to extended ones over the whole section, to obtain different dynamic nonreciprocal effects. Simulations illustrate how the combination of bilinearity and spatial asymmetry ensures a passive amplitude-independent nonreciprocal 2D system for a variety of different excitations.
Highlights
Reciprocity is a fundamental physical principle of wave motion that guarantees symmetric wave transmission between a source and a receiver
Breaking reciprocity in one-dimensional (1D) structures can be achieved in many different ways, either using external energy to modulate the system properties or introducing nonlinearity with spatial asymmetry
By introducing bilinearity with spatial asymmetry in a place that a wave can reach from the source, see Fig. 3(b), a signal will travel from the source to the receiver via scattering from the bilinear section
Summary
Reciprocity is a fundamental physical principle of wave motion that guarantees symmetric wave transmission between a source and a receiver. Breaking reciprocity in one-dimensional (1D) structures can be achieved in many different ways, either using external energy to modulate the system properties (active methods) or introducing nonlinearity with spatial asymmetry (passive methods). Nonreciprocal transmission of Rayleigh surface waves with one-way mode conversion can be realized in a continuous 2D semi-infinite medium bound with an array of space–time modulated spring–mass oscillators [22] Both the topological insulators and the semi-infinite medium with complex interface are active nonreciprocal systems which require external energy input, and as a consequence they are potentially unstable. (a) and (b) depict the physical structure of a unit cell in the monatomic lattice, which consists of a block with mass and a mass-less ”+” shape structure of size d → 0 introducing the in-plane transverse wave propagation; (a) stands for the state of ”+” shape up and (b) down. A1 κ1 sin k1a1 where the values of k1 and k2 are specified by the isofrequency contour of Fig. 2(b) for a selected frequency ω
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